For much of the past two weeks, as Rick Santorum’s candidacy star power has increased, so too have his critiques of public education. At recent campaign events and in last Thursday’s debate, he called American public schools “big factories” left over from the Industrial Revolution and argued for decreasing federal and state roles in education. “Yes, the government can help,” he said at an event in Ohio. “But the idea that the federal government should be running schools, frankly much less that the state government should be running schools, is anachronistic.”

Santorum is hardly the first presidential candidate to call for a decreased federal role in schools. Ron Paul, Michele Bachmann and Rick Perry before him called for abolishing the Department of Education, while Newt Gingrich has said he would dramatically shrink the department and remove all of the regulations it imposes. Mitt Romney is the only candidate left who has spoken favorably about the department; in 2007 he said he had come to see the value of having a federal role in education because it helped hold down the interests of the teachers’ unions by putting students and parents first. (He did suggest abolishing the Department of Education in the 1990s.)

But few have been more openly critical of public education than Santorum, and his rhetoric often fails to match up with reality — and his own record. During his tenure in the Senate, Santorum voted for an increased federal role in schools and a larger budget for the Department of Education. Michael Tennant of the New Americanparsed his voting record and found that in addition to voting in favor of George W. Bush’s No Child Left Behind act, a vote Santorum now says he regrets, he voted in 2001 to increase federal funding for teacher testing and to up the Department of Education’s budget by $3.1 billion in 1996.

Here are the three things Santorum apparently doesn’t know (or disregards) about public education:

Presidents have not historically educated their kids at home.
Santorum has said he would homeschool his children in the White House like, as he claims, most Presidents did in the first 150 years of the nation’s history. But as Andy Horowitz writes, of the very few Presidents who had school-age kids during their Administrations, most sent their children to public schools, military academies or private prep schools. Additionally, Thomas Jefferson was so wild about public education that he founded the University of Virginia, a public college, and said education should be available to all “without regard to wealth, birth or other accidental condition or circumstance. Further, he wrote, “It is better such should be sought for and educated at the common expence [sic] of all, than that the happiness of all should be confided to the weak or wicked.”

The federal role in public education isn’t enormous.
For all Santorum’s desire to pull back federal education funding, it makes up only about 11% of all public-education spending. The vast majority of funds for education come from individual states and, to a lesser degree, local school boards. And while the federal money might be a small portion of school budgets, federal funding requirements play an important role. Historically, when left to their own devices, states have not always done a good job of educating their young people. Some states do it well, while others fall behind. Federal dollars — and the strings attached to them — are designed to ensure children can get the same quality of education whether they are born in Massachusetts or Mississippi.

Homeschooling doesn’t work for everyone.
Santorum hasn’t said he would push for homeschooling for all, but in criticizing public education while touting the fact that his seven kids are homeschooled, he seems to imply that it’s the better option. In Ohio, he even went as far as to say, “Parents educated their children because it’s their responsibility to educate their children.” That’s all well and good if you’re Santorum. He’s well off — having brought in $660,000 to $1.1 million in income in each of the past four years — which means his family could afford to have one parent stay home with the children or hire a tutor to come to the home. When he was a Senator, Santorum enrolled five of his children in an online charter school and had Pennsylvania taxpayers foot the $100,000 bill (creating an uproar so loud that he later withdrew them).

Santorum also has a rich educational background to draw on, having attended Pennsylvania State University for his undergraduate degree and received an MBA from the University of Pittsburgh and a subsequent law degree from Penn State. (Both are publicly funded colleges, mind you.) But unlike Santorum, many parents do not have the educational background to teach their own kids. It’s still quite common for children to be more educated than their parents, particularly if they come from impoverished immigrant communities. (Santorum is himself a child of immigrants.) Since it is impossible to impart educational wisdom if you yourself are not educated, a broader-scale homeschooling system would only exacerbate educational inequality in the nation.

Virtually no one — not even the most fervent education supporters — would claim that everything is going great today in America’s public-education system. Compared with other economically developed countries worldwide, students in the U.S. are average at best. Despite its admirable intentions, teachers and administrators say No Child Left Behind set impossibly high standards, narrowed curriculums, forced educators to teach to the test and labeled far too many schools as “in need of improvement.” The Obama Administration is even giving out waivers to let states off the hook, in exchange for their adopting the Administration’s preferred set of education reforms. Yet the waivers are just a stopgap measure. Whoever is elected President in 2012 will have the opportunity to preside over what could be the greatest change to federal education policy since NCLB was adopted in 2001 — should Congress decide to take up the task of reworking NCLB, which been due for reauthorization since 2007. Whoever that person is should have his facts straight about public education.

Kayla Webley is a staff writer at TIME. Find her on Twitter at @kaylawebley, on Facebook or on Google+. You can also continue the discussion on TIME’s Facebook page and on Twitter at @TIME.